Currently, there exists a lack of geometric visualization in the student's comprehension of three-dimensional concepts in multivariable calculus. Unfortunately, this in turn makes it difficult for the student to understand the basic calculations involved in math and engineering classes. For example, most students are confused about the signs of the first and second derivatives in various directions, when confronted with a picture of a surface on an exam. They are unable to determine the slope of the line between two points in 3D. Nor could they easily determine which integral is larger when given two surfaces, one clearly above the other.
Computer software has provided enormous aids to students and professors wishing to visualize concepts in three dimensions. However, there are many concepts where the two dimensional nature of a computer screen can limit the effectiveness of these packages; particularly if students have a weak geometric background. For example, directional derivatives require the tangent line to a surface in a direction associated with the xy plane. In three dimensions, a surface can be placed over the xy plane, the direction on the xy plane can be indicated and the concept can be visualized quite easily. However, visualizing a precise direction and its associated tangent line on a 2D computer screen is often difficult for students. Correspondingly, a more effective pedagogical approach is to use physical 3D manipulatives. These allow visualization and motivation of, concepts in a real three dimensional space. Particularly when students are first being introduced to multivariable functions, this often proves more effective than a projection of three dimensions onto a two dimensional computer screen.
Thus, what is needed, is a simple, hands-on 3D tool for use as aid in teaching these concepts.